Shi Haodong, Jiang Huilin, Zhang Xin, Wang Chao, Liu Tao
Appl Opt. 2016 Aug 20;55(24):6782-90. doi: 10.1364/AO.55.006782.
Freeform surfaces have the advantage of balancing off-axis aberration. In this paper, based on the framework of nodal aberration theory (NAT) applied to the coaxial system, the third-order astigmatism and coma wave aberration expressions of an off-axis system with Zernike polynomial surfaces are derived. The relationship between the off-axis and surface shape acting on the nodal distributions is revealed. The nodal aberration properties of the off-axis freeform system are analyzed and validated by using full-field displays (FFDs). It has been demonstrated that adding Zernike terms, up to nine, to the off-axis system modifies the nodal locations, but the field dependence of the third-order aberration does not change. On this basis, an off-axis two-mirror freeform system with 500 mm effective focal length (EFL) and 300 mm entrance pupil diameter (EPD) working in long-wave infrared is designed. The field constant aberrations induced by surface tilting are corrected by selecting specific Zernike terms. The design results show that the nodes of third-order astigmatism and coma move back into the field of view (FOV). The modulation transfer function (MTF) curves are above 0.4 at 20 line pairs per millimeter (lp/mm) which meets the infrared reconnaissance requirement. This work provides essential insight and guidance for aberration correction in off-axis freeform system design.
自由曲面具有平衡离轴像差的优势。本文基于应用于同轴系统的节点像差理论（NAT）框架，推导了具有泽尼克多项式曲面的离轴系统的三阶像散和彗差波像差表达式。揭示了离轴与作用于节点分布的表面形状之间的关系。利用全场显示（FFD）对离轴自由曲面系统的节点像差特性进行了分析和验证。结果表明，在离轴系统中添加多达九项的泽尼克项会改变节点位置，但三阶像差的场依赖性不变。在此基础上，设计了一种工作在长波红外波段、有效焦距（EFL）为500 mm、入瞳直径（EPD）为300 mm的离轴双镜自由曲面系统。通过选择特定的泽尼克项来校正由表面倾斜引起的场常数像差。设计结果表明，三阶像散和彗差的节点移回到视场（FOV）内。调制传递函数（MTF）曲线在每毫米20线对（lp/mm）时高于0.4，满足红外侦察要求。这项工作为离轴自由曲面系统设计中的像差校正提供了重要的见解和指导。
